facility location problem

ENDÜSTRİDE BİLGİSAYAR ENDÜSTRİDE BİLGİSAYAR UYGULAMALARI - 2UYGULAMALARI - 2

New potential hubs in the South-New potential hubs in the South-Atlantic market. A problem of Atlantic market. A problem of

locationlocation

JournalJournal of of TransportTransport GeographyGeography

Volume 11, Issue 2 , June 2003, Pages 139-149Volume 11, Issue 2 , June 2003, Pages 139-149

FERİDE SEVLİ – 2000503052FERİDE SEVLİ – 2000503052AYTÜL ŞENER – 200503056AYTÜL ŞENER – 200503056

İLKEM YALINER – 2000503067İLKEM YALINER – 2000503067

İçerik:İçerik:

• Tesis Planlama KavramıTesis Planlama Kavramı

• Tesis Planlamanın AmaçlarıTesis Planlamanın Amaçları

• Tesis Planlama TipleriTesis Planlama Tipleri

• Tesisin Kurulacağı Bölgenin SeçimiTesisin Kurulacağı Bölgenin Seçimi

• Alternatiflerin Değerlendirilme Alternatiflerin Değerlendirilme YöntemleriYöntemleri

• Havacılık Sektöründe Tesis Planlama Havacılık Sektöründe Tesis Planlama UygulamalarıUygulamaları

TESİS PLANLAMA KAVRAMI:TESİS PLANLAMA KAVRAMI:

• TESİS : TESİS : Mal ve hizmetlerin fiilen Mal ve hizmetlerin fiilen üretildiği fiziksel birimlerdir. üretildiği fiziksel birimlerdir.

• TESİS PLANLAMA :TESİS PLANLAMA : Tesislerin Tesislerin düzenleme çalışmalarının yapılması, düzenleme çalışmalarının yapılması, tesisin kurulması ve faaliyete tesisin kurulması ve faaliyete geçirilmesi aşamalarında geçirilmesi aşamalarında gerçekleştirilecek olan faaliyetlerin gerçekleştirilecek olan faaliyetlerin bugünden eşgüdümlerinin yapılmasıdır.bugünden eşgüdümlerinin yapılmasıdır.

TESİS PLANLAMA AMAÇLARI:TESİS PLANLAMA AMAÇLARI:

Kaynakların kullanımıKaynakların kullanımı Darboğazların belirlenmesiDarboğazların belirlenmesi Tesis faaliyetleri Tesis faaliyetleri

Optimum yerleşim düzeniOptimum yerleşim düzeniMaliyetMaliyetMesafeMesafeZamanZaman

TESİS PLANLAMA TİPLERİ:TESİS PLANLAMA TİPLERİ:

• Basit Yerleşim Basit Yerleşim

• Çoklu YerleşimÇoklu Yerleşim

• Tesis Oluşturulması ve Kapasite AtamaTesis Oluşturulması ve Kapasite Atama

• Tesis Seçimi ve Kapasite Atama Tesis Seçimi ve Kapasite Atama

• Tesis İçi Yerleşim(QAP)Tesis İçi Yerleşim(QAP)

TESİSİN KURULACAĞI TESİSİN KURULACAĞI BÖLGENİN SEÇİLMESİ:BÖLGENİN SEÇİLMESİ:Yerleşim Kararlarını Etkileyen Yerleşim Kararlarını Etkileyen

Faktörler :Faktörler :

• Ülke seçimi (kanunlar, pazar, Ülke seçimi (kanunlar, pazar, işgücü, tedarik, alım gücü vb.)işgücü, tedarik, alım gücü vb.)

• Bölge seçimi (maliyet, çevre Bölge seçimi (maliyet, çevre kuralları, müşteri&hammadde kuralları, müşteri&hammadde erişimi vb.)erişimi vb.)

• Yer seçimi (yerin alan&maliyeti, Yer seçimi (yerin alan&maliyeti, ulaşım kolaylığı vb.)ulaşım kolaylığı vb.)

ALTERNATİFLERİ ALTERNATİFLERİ DEĞERLENDİRMEDEĞERLENDİRME YÖNTEMLERİ:YÖNTEMLERİ:

– Faktör Oranlama Metodu Faktör Oranlama Metodu – Başa-baş AnaliziBaşa-baş Analizi– Ağırlık Merkezi MetoduAğırlık Merkezi Metodu– Ulaştırma MetoduUlaştırma Metodu

Problem:Problem:

Güney Amerika–Avrupa arasındaGüney Amerika–Avrupa arasında

düzenlenen uçuş seferlerinde optimumdüzenlenen uçuş seferlerinde optimum

aktarma noktası seçimiaktarma noktası seçimi

Veriler:Veriler:

1) Şehirler arası mesafeler1) Şehirler arası mesafeler

TOTOFROMFROM

LİSBONLİSBON MADRIDMADRID PARISPARIS SANTIAGOSANTIAGO SAO PAULOSAO PAULO BUONES AIRESBUONES AIRES

LISBONLISBON 00 10001000 32003200 2400024000 1760017600 2110021100

MADRIDMADRID 10001000 00 25002500 2400024000 1950019500 2310023100

PARISPARIS 32003200 25002500 00 2620026200 2110021100 2440024400

SANTIAGOSANTIAGO 2400024000 2400024000 2620026200 00 70007000 41004100

SAO PAULOSAO PAULO 1760017600 1950019500 2110021100 70007000 00 40004000

BUONES AIRESBUONES AIRES 2110021100 2310023100 2440024400 41004100 40004000 00

Veriler:Veriler:

2) Şehirler arası yolcu sayısı2) Şehirler arası yolcu sayısı

TO TO FROMFROM

LİSBONLİSBON MADRIDMADRID PARISPARIS SANTIAGOSANTIAGO SAO PAULOSAO PAULO BUONES AIRESBUONES AIRES

LISBONLISBON 00 00 00 6200062000 6923869238 121000121000

MADRIDMADRID 00 00 00 8122081220 126137126137 240213240213

PARISPARIS 00 00 00 7400074000 155036155036 8500085000

SANTIAGOSANTIAGO 9500095000 8005480054 8200082000 00 00 00

SAO PAULOSAO PAULO 7384773847 126851126851 143977143977 00 00 00

BUONES AIRESBUONES AIRES 110000110000 270051270051 8300083000 00 00 00

min Σ (d Ei Hx + d Hx Sj ) T Ei Sj

HxEuS Ei E T *

Sj S

Problemin Lingo Modeli:Problemin Lingo Modeli:• SETS:SETS:• AIRPORT/LISBON MADRID PARIS SANTIAGO SAOPAULO BUONESAIRES/:HUB,K;AIRPORT/LISBON MADRID PARIS SANTIAGO SAOPAULO BUONESAIRES/:HUB,K;• A(AIRPORT,AIRPORT):DIST,PASS;A(AIRPORT,AIRPORT):DIST,PASS;• ENDSETSENDSETS• DATA:DATA:• DIST=0 1000 3200 24000 17600 21100 DIST=0 1000 3200 24000 17600 21100 • 1000 0 2500 24000 19500 23100 1000 0 2500 24000 19500 23100 • 3200 2500 0 26200 21100 244003200 2500 0 26200 21100 24400• 24000 24000 26200 0 7000 410024000 24000 26200 0 7000 4100• 17600 19500 21100 7000 0 400017600 19500 21100 7000 0 4000• 21100 23100 24400 4100 4000 0 ;21100 23100 24400 4100 4000 0 ;• PASS=0 0 0 62000 69238 121000 PASS=0 0 0 62000 69238 121000 • 0 0 0 81220 126137 240213 0 0 0 81220 126137 240213 • 0 0 0 74000 155036 850000 0 0 74000 155036 85000• 95000 80054 82000 0 0 0 95000 80054 82000 0 0 0 • 73847 126851 143977 0 0 073847 126851 143977 0 0 0• 110000 270051 83000 0 0 0 ;110000 270051 83000 0 0 0 ;• ENDDATAENDDATA• MIN=@SUM(AIRPORT(I):HUB(I)*K(I));MIN=@SUM(AIRPORT(I):HUB(I)*K(I));• @FOR(AIRPORT(I):@SUM(A(J,K)|J#NE#I #AND# #NE#K:(DIST(J,I)@FOR(AIRPORT(I):@SUM(A(J,K)|J#NE#I #AND# #NE#K:(DIST(J,I)

+DIST(I,K))*PASS(J,K))=HUB(I));+DIST(I,K))*PASS(J,K))=HUB(I));• IFA=@MIN(AIRPORT(I):HUB(I));IFA=@MIN(AIRPORT(I):HUB(I));• @FOR(AIRPORT(I)|HUB(I)#LE#IFA:K(I)=1);@FOR(AIRPORT(I)|HUB(I)#LE#IFA:K(I)=1);• @FOR(AIRPORT(I):@BIN(K(I)));@FOR(AIRPORT(I):@BIN(K(I)));

Lingo Çözümü:Lingo Çözümü:• Rows= 1 Vars= 5 No. integer vars= 5 ( all are linear)Rows= 1 Vars= 5 No. integer vars= 5 ( all are linear)• Nonzeros= 6 Constraint nonz= 0( 0 are +- 1) Density=1.000Nonzeros= 6 Constraint nonz= 0( 0 are +- 1) Density=1.000• Smallest and largest elements in absolute value= 0.317284E+11 0.481254ESmallest and largest elements in absolute value= 0.317284E+11 0.481254E• No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0• Single cols= 5Single cols= 5• Optimal solution found at step: 0Optimal solution found at step: 0• Objective value: 0.2743843E+11Objective value: 0.2743843E+11• Branch count: 0Branch count: 0• Variable Variable Value Value Reduced CostReduced Cost• IFA IFA 0.2743843E+11 0.2743843E+11 0.0000000E+000.0000000E+00• HUB( LISBON) HUB( LISBON) 0.3455933E+11 0.3455933E+11 0.0000000E+000.0000000E+00• HUB( MADRID) HUB( MADRID) 0.2743843E+11 0.2743843E+11 0.0000000E+000.0000000E+00• HUB( PARIS) HUB( PARIS) 0.3879355E+11 0.3879355E+11 0.0000000E+000.0000000E+00• HUB( SANTIAGO) HUB( SANTIAGO) 0.4812541E+11 0.4812541E+11 0.0000000E+000.0000000E+00• HUB( SAOPAULO) HUB( SAOPAULO) 0.3371716E+11 0.3371716E+11 0.0000000E+000.0000000E+00• HUB( BUONESAIRES) HUB( BUONESAIRES) 0.3172843E+11 0.3172843E+11 0.0000000E+000.0000000E+00• K( LISBON) K( LISBON) 0.0000000E+00 0.0000000E+00 0.3455933E+110.3455933E+11• K( MADRID) K( MADRID) 1.000000 1.000000 0.0000000E+000.0000000E+00• K( PARIS) K( PARIS) 0.0000000E+00 0.0000000E+00 0.3879355E+110.3879355E+11• K( SANTIAGO) K( SANTIAGO) 0.0000000E+00 0.0000000E+00 0.4812541E+110.4812541E+11• K( SAOPAULO) K( SAOPAULO) 0.0000000E+00 0.0000000E+00 0.3371716E+110.3371716E+11• K( BUONESAIRES) K( BUONESAIRES) 0.0000000E+00 0.0000000E+00 0.3172843E+110.3172843E+11

Lingo Çözümü:Lingo Çözümü:• DIST( LISBON, LISBON) DIST( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( LISBON, MADRID) DIST( LISBON, MADRID) 1000.000 1000.000 0.0000000E+000.0000000E+00• DIST( LISBON, PARIS) DIST( LISBON, PARIS) 3200.000 3200.000 0.0000000E+000.0000000E+00• DIST( LISBON, SANTIAGO) DIST( LISBON, SANTIAGO) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( LISBON, SAOPAULO) DIST( LISBON, SAOPAULO) 17600.00 17600.00 0.0000000E+000.0000000E+00• DIST( LISBON, BUONESAIRES) DIST( LISBON, BUONESAIRES) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( MADRID, LISBON) DIST( MADRID, LISBON) 1000.000 1000.000 0.0000000E+000.0000000E+00• DIST( MADRID, MADRID) DIST( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( MADRID, PARIS) DIST( MADRID, PARIS) 2500.000 2500.000 0.0000000E+000.0000000E+00• DIST( MADRID, SANTIAGO) DIST( MADRID, SANTIAGO) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( MADRID, SAOPAULO) DIST( MADRID, SAOPAULO) 19500.00 19500.00 0.0000000E+000.0000000E+00• DIST( MADRID, BUONESAIRES) DIST( MADRID, BUONESAIRES) 23100.00 23100.00 0.0000000E+000.0000000E+00• DIST( PARIS, LISBON) DIST( PARIS, LISBON) 3200.000 3200.000 0.0000000E+000.0000000E+00• DIST( PARIS, MADRID) DIST( PARIS, MADRID) 2500.000 2500.000 0.0000000E+000.0000000E+00• DIST( PARIS, PARIS) DIST( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( PARIS, SANTIAGO) DIST( PARIS, SANTIAGO) 26200.00 26200.00 0.0000000E+000.0000000E+00• DIST( PARIS, SAOPAULO) DIST( PARIS, SAOPAULO) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( PARIS, BUONESAIRES)DIST( PARIS, BUONESAIRES) 24400.00 24400.00 0.0000000E+000.0000000E+00• DIST( SANTIAGO, LISBON) DIST( SANTIAGO, LISBON) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( SANTIAGO, MADRID) DIST( SANTIAGO, MADRID) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( SANTIAGO, PARIS) DIST( SANTIAGO, PARIS) 26200.00 26200.00 0.0000000E+000.0000000E+00• DIST( SANTIAGO, SANTIAGO)DIST( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( SANTIAGO, SAOPAULO)DIST( SANTIAGO, SAOPAULO) 7000.000 7000.000 0.0000000E+000.0000000E+00• DIST( SANTIAGO, BUONESAIRES) DIST( SANTIAGO, BUONESAIRES) 4100.000 4100.000 0.0000000E+000.0000000E+00

Lingo Çözümü:Lingo Çözümü:• DIST( SAOPAULO, LISBON) DIST( SAOPAULO, LISBON) 17600.00 17600.00 0.0000000E+000.0000000E+00• DIST( SAOPAULO, MADRID) DIST( SAOPAULO, MADRID) 19500.00 19500.00 0.0000000E+000.0000000E+00• DIST( SAOPAULO, PARIS) DIST( SAOPAULO, PARIS) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( SAOPAULO, SANTIAGO) DIST( SAOPAULO, SANTIAGO) 7000.000 7000.000 0.0000000E+000.0000000E+00• DIST( SAOPAULO, SAOPAULO) DIST( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( SAOPAULO, BUONESAIRES) DIST( SAOPAULO, BUONESAIRES) 4000.000 4000.000 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, LISBON) DIST( BUONESAIRES, LISBON) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, MADRID) DIST( BUONESAIRES, MADRID) 23100.00 23100.00 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, PARIS) DIST( BUONESAIRES, PARIS) 24400.00 24400.00 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, SANTIAGO) DIST( BUONESAIRES, SANTIAGO) 4100.000 4100.000 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, SAOPAULO) DIST( BUONESAIRES, SAOPAULO) 4000.000 4000.000 0.0000000E+000.0000000E+00• DIST( BUONESAIRES, BUONESAIRES DIST( BUONESAIRES, BUONESAIRES 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( LISBON, LISBON) PASS( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( LISBON, MADRID) PASS( LISBON, MADRID) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( LISBON, PARIS) PASS( LISBON, PARIS) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( LISBON, SANTIAGO) PASS( LISBON, SANTIAGO) 62000.00 62000.00 0.0000000E+000.0000000E+00• PASS( LISBON, SAOPAULO) PASS( LISBON, SAOPAULO) 69238.00 69238.00 0.0000000E+000.0000000E+00• PASS( LISBON, BUONESAIRES) PASS( LISBON, BUONESAIRES) 121000.0 121000.0 0.0000000E+000.0000000E+00• PASS( MADRID, LISBON) PASS( MADRID, LISBON) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( MADRID, MADRID) PASS( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( MADRID, PARIS) PASS( MADRID, PARIS) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( MADRID, SANTIAGO) PASS( MADRID, SANTIAGO) 81220.00 81220.00 0.0000000E+000.0000000E+00• PASS( MADRID, SAOPAULO) PASS( MADRID, SAOPAULO) 126137.0 126137.0 0.0000000E+000.0000000E+00• PASS( MADRID, BUONESAIRES) PASS( MADRID, BUONESAIRES) 240213.0 240213.0 0.0000000E+000.0000000E+00

Lingo Çözümü:Lingo Çözümü:• PASS( PARIS, LISBON) PASS( PARIS, LISBON) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( PARIS, MADRID) PASS( PARIS, MADRID) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( PARIS, PARIS) PASS( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( PARIS, SANTIAGO) PASS( PARIS, SANTIAGO) 74000.00 74000.00 0.0000000E+000.0000000E+00• PASS( PARIS, SAOPAULO) PASS( PARIS, SAOPAULO) 155036.0 155036.0 0.0000000E+000.0000000E+00• PASS( PARIS, BUONESAIRES) PASS( PARIS, BUONESAIRES) 85000.00 85000.00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, LISBON) PASS( SANTIAGO, LISBON) 95000.00 95000.00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, MADRID) PASS( SANTIAGO, MADRID) 80054.00 80054.00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, PARIS) PASS( SANTIAGO, PARIS) 82000.00 82000.00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, SANTIAGO) PASS( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, SAOPAULO) PASS( SANTIAGO, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( SANTIAGO, BUONESAIRES) 0.0000000E+00 PASS( SANTIAGO, BUONESAIRES) 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( SAOPAULO, LISBON) PASS( SAOPAULO, LISBON) 73847.00 73847.00 0.0000000E+000.0000000E+00• PASS( SAOPAULO, MADRID) PASS( SAOPAULO, MADRID) 126851.0 126851.0 0.0000000E+000.0000000E+00• PASS( SAOPAULO, PARIS) PASS( SAOPAULO, PARIS) 143977.0 143977.0 0.0000000E+000.0000000E+00• PASS( SAOPAULO, SANTIAGO) PASS( SAOPAULO, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( SAOPAULO, SAOPAULO) PASS( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( SAOPAULO, BUONESAIRES) 0.0000000E+00 PASS( SAOPAULO, BUONESAIRES) 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, LISBON) PASS( BUONESAIRES, LISBON) 110000.0 110000.0 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, MADRID) PASS( BUONESAIRES, MADRID) 270051.0 270051.0 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, PARIS) PASS( BUONESAIRES, PARIS) 83000.00 83000.00 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, SANTIAGO) 0.0000000E+00 PASS( BUONESAIRES, SANTIAGO) 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, SAOPAULO) PASS( BUONESAIRES, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• PASS( BUONESAIRES, BUONESAIRES PASS( BUONESAIRES, BUONESAIRES 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00

Lingo Çözümü:Lingo Çözümü:

• Row Slack or Surplus Dual PriceRow Slack or Surplus Dual Price• 1 0.2743843E+11 -1.0000001 0.2743843E+11 -1.000000• 2 0.0000000E+00 0.0000000E+002 0.0000000E+00 0.0000000E+00• 3 0.0000000E+00 1.0000003 0.0000000E+00 1.000000• 4 0.0000000E+00 0.0000000E+004 0.0000000E+00 0.0000000E+00• 5 0.0000000E+00 0.0000000E+005 0.0000000E+00 0.0000000E+00• 6 0.0000000E+00 0.0000000E+006 0.0000000E+00 0.0000000E+00• 7 0.0000000E+00 0.0000000E+007 0.0000000E+00 0.0000000E+00• 8 0.0000000E+00 0.0000000E+008 0.0000000E+00 0.0000000E+00• 9 0.0000000E+00 -0.2743843E+119 0.0000000E+00 -0.2743843E+11

Problem:Problem:

Avrupa – Güney Amerika arasındaAvrupa – Güney Amerika arasında

düzenlenen uçuş seferlerinde; biri düzenlenen uçuş seferlerinde; biri AmerikaAmerika

diğeri Avrupa’da olmak üzere iki tanediğeri Avrupa’da olmak üzere iki tane

aktarma noktası seçimiaktarma noktası seçimi

min Σ (d EjEx + d ExSy + d SySj ) T Ei Sj

Ex,SyExS Ei E T * Sj S

Problemin Lingo Modeli:Problemin Lingo Modeli:• SETS:SETS:• S1/LISBON MADRID PARIS/;S1/LISBON MADRID PARIS/;• S2/SANTIAGO SAOPAULO BUONESAIRES/;S2/SANTIAGO SAOPAULO BUONESAIRES/;• B1(S1,S1):DIST1;B1(S1,S1):DIST1;• B2(S2,S2):DIST2;B2(S2,S2):DIST2;• A(S1,S2):DIST,PASS,HUB,AFI;A(S1,S2):DIST,PASS,HUB,AFI;• ENDSETSENDSETS• DATA:DATA:• DIST1= 0 1000 3200DIST1= 0 1000 3200• 1000 0 25001000 0 2500• 3200 2500 0 ;3200 2500 0 ;• DIST2= 0 7000 4100DIST2= 0 7000 4100• 7000 0 40007000 0 4000• 4100 4000 0 ;4100 4000 0 ;• DIST= 24000 17600 21100DIST= 24000 17600 21100• 24000 19500 2310024000 19500 23100• 26200 21100 24400;26200 21100 24400;• PASS= 157000 143085 231000PASS= 157000 143085 231000• 161274 252988 425087161274 252988 425087• 156000 384190 168000;156000 384190 168000;• ENDDATAENDDATA• MIN=@SUM(A(I,J):HUB(I,J)*AFI(I,J));MIN=@SUM(A(I,J):HUB(I,J)*AFI(I,J));• @FOR(A(I,J):@SUM(A(K,L):(DIST1(K,I)+DIST(I,J)+DIST2(J,L))*PASS(K,L))=HUB(I,J));@FOR(A(I,J):@SUM(A(K,L):(DIST1(K,I)+DIST(I,J)+DIST2(J,L))*PASS(K,L))=HUB(I,J));• IFA=@MIN(A(I,L):HUB(I,L));IFA=@MIN(A(I,L):HUB(I,L));• @FOR(A(M,N)|HUB(M,N)#LE#IFA:AFI(M,N)=1);@FOR(A(M,N)|HUB(M,N)#LE#IFA:AFI(M,N)=1);• @FOR(A(I,J):@BIN(AFI(I,J)));@FOR(A(I,J):@BIN(AFI(I,J)));

Lingo Çözümü:Lingo Çözümü:

• Rows= 1 Vars= 8 No. integer vars= 8 ( all are linear)Rows= 1 Vars= 8 No. integer vars= 8 ( all are linear)• Nonzeros= 9 Constraint nonz= 0( 0 are +- 1) Density=1.000Nonzeros= 9 Constraint nonz= 0( 0 are +- 1) Density=1.000• Smallest and largest elements in absolute value= 0.494510E+11 0.670984ESmallest and largest elements in absolute value= 0.494510E+11 0.670984E• No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0• Single cols= 8Single cols= 8• Optimal solution found at step: 0Optimal solution found at step: 0• Objective value: 0.4630561E+11Objective value: 0.4630561E+11• Branch count: 0Branch count: 0

• Variable Variable Value Value Reduced Cost Reduced Cost• IFA IFA 0.4630561E+11 0.4630561E+11 0.0000000E+000.0000000E+00• DIST1( LISBON, LISBON) DIST1( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST1( LISBON, MADRID) DIST1( LISBON, MADRID) 1000.000 1000.000 0.0000000E+000.0000000E+00• DIST1( LISBON, PARIS) DIST1( LISBON, PARIS) 3200.000 3200.000 0.0000000E+000.0000000E+00• DIST1( MADRID, LISBON) DIST1( MADRID, LISBON) 1000.000 1000.000 0.0000000E+000.0000000E+00• DIST1( MADRID, MADRID) DIST1( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST1( MADRID, PARIS) DIST1( MADRID, PARIS) 2500.000 2500.000 0.0000000E+000.0000000E+00• DIST1( PARIS, LISBON) DIST1( PARIS, LISBON) 3200.000 3200.000 0.0000000E+000.0000000E+00• DIST1( PARIS, MADRID) DIST1( PARIS, MADRID) 2500.000 2500.000 0.0000000E+000.0000000E+00• DIST1( PARIS, PARIS) DIST1( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00

Lingo Çözümü:Lingo Çözümü:• DIST2( SANTIAGO, SANTIAGO) DIST2( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST2( SANTIAGO, SAOPAULO) DIST2( SANTIAGO, SAOPAULO) 7000.000 7000.000 0.0000000E+000.0000000E+00• DIST2( SANTIAGO, BUONESAIRES) DIST2( SANTIAGO, BUONESAIRES) 4100.000 4100.000 0.0000000E+000.0000000E+00• DIST2( SAOPAULO, SANTIAGO) DIST2( SAOPAULO, SANTIAGO) 7000.000 7000.000 0.0000000E+000.0000000E+00• DIST2( SAOPAULO, SAOPAULO) DIST2( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST2( SAOPAULO, BUONESAIRES) DIST2( SAOPAULO, BUONESAIRES) 4000.000 4000.000 0.0000000E+000.0000000E+00• DIST2( BUONESAIRES, SANTIAGO) DIST2( BUONESAIRES, SANTIAGO) 4100.000 4100.000 0.0000000E+000.0000000E+00• DIST2( BUONESAIRES, SAOPAULO) DIST2( BUONESAIRES, SAOPAULO) 4000.000 4000.000 0.0000000E+000.0000000E+00• DIST2( BUONESAIRES, BUONESAIRE DIST2( BUONESAIRES, BUONESAIRE 0.0000000E+00 0.0000000E+00 0.0000000E+000.0000000E+00• DIST( LISBON, SANTIAGO) DIST( LISBON, SANTIAGO) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( LISBON, SAOPAULO) DIST( LISBON, SAOPAULO) 17600.00 17600.00 0.0000000E+000.0000000E+00• DIST( LISBON, BUONESAIRES) DIST( LISBON, BUONESAIRES) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( MADRID, SANTIAGO) DIST( MADRID, SANTIAGO) 24000.00 24000.00 0.0000000E+000.0000000E+00• DIST( MADRID, SAOPAULO) DIST( MADRID, SAOPAULO) 19500.00 19500.00 0.0000000E+000.0000000E+00• DIST( MADRID, BUONESAIRES) DIST( MADRID, BUONESAIRES) 23100.00 23100.00 0.0000000E+000.0000000E+00• DIST( PARIS, SANTIAGO) DIST( PARIS, SANTIAGO) 26200.00 26200.00 0.0000000E+000.0000000E+00• DIST( PARIS, SAOPAULO) DIST( PARIS, SAOPAULO) 21100.00 21100.00 0.0000000E+000.0000000E+00• DIST( PARIS, BUONESAIRES) DIST( PARIS, BUONESAIRES) 24400.00 24400.00 0.0000000E+000.0000000E+00• PASS( LISBON, SANTIAGO) PASS( LISBON, SANTIAGO) 157000.0 157000.0 0.0000000E+000.0000000E+00• PASS( LISBON, SAOPAULO) PASS( LISBON, SAOPAULO) 143085.0 143085.0 0.0000000E+000.0000000E+00• PASS( LISBON, BUONESAIRES) PASS( LISBON, BUONESAIRES) 231000.0 231000.0 0.0000000E+000.0000000E+00• PASS( MADRID, SANTIAGO) PASS( MADRID, SANTIAGO) 161274.0 161274.0 0.0000000E+000.0000000E+00• PASS( MADRID, SAOPAULO) PASS( MADRID, SAOPAULO) 252988.0 252988.0 0.0000000E+000.0000000E+00• PASS( MADRID, BUONESAIRES) PASS( MADRID, BUONESAIRES) 425087.0 425087.0 0.0000000E+000.0000000E+00

Lingo Çözümü:Lingo Çözümü:• PASS( PARIS, SANTIAGO) PASS( PARIS, SANTIAGO) 156000.0 156000.0 0.0000000E+000.0000000E+00• PASS( PARIS, SAOPAULO) PASS( PARIS, SAOPAULO) 384190.0 384190.0 0.0000000E+000.0000000E+00• PASS( PARIS, BUONESAIRES) PASS( PARIS, BUONESAIRES) 168000.0 168000.0 0.0000000E+000.0000000E+00• HUB( LISBON, SANTIAGO) HUB( LISBON, SANTIAGO) 0.6183313E+11 0.6183313E+11 0.0000000E+000.0000000E+00• HUB( LISBON, SAOPAULO) HUB( LISBON, SAOPAULO) 0.4630561E+11 0.4630561E+11 0.0000000E+000.0000000E+00• HUB( LISBON, BUONESAIRES) HUB( LISBON, BUONESAIRES) 0.5203010E+11 0.5203010E+11 0.0000000E+000.0000000E+00• HUB( MADRID, SANTIAGO) HUB( MADRID, SANTIAGO) 0.6102913E+11 0.6102913E+11 0.0000000E+000.0000000E+00• HUB( MADRID, SAOPAULO) HUB( MADRID, SAOPAULO) 0.4945099E+11 0.4945099E+11 0.0000000E+000.0000000E+00• HUB( MADRID, BUONESAIRES) HUB( MADRID, BUONESAIRES) 0.5538335E+11 0.5538335E+11 0.0000000E+000.0000000E+00• HUB( PARIS, SANTIAGO) HUB( PARIS, SANTIAGO) 0.6709839E+11 0.6709839E+11 0.0000000E+000.0000000E+00• HUB( PARIS, SAOPAULO) HUB( PARIS, SAOPAULO) 0.5427308E+11 0.5427308E+11 0.0000000E+000.0000000E+00• HUB( PARIS, BUONESAIRES) HUB( PARIS, BUONESAIRES) 0.5958185E+11 0.5958185E+11 0.0000000E+000.0000000E+00• AFI( LISBON, SANTIAGO) AFI( LISBON, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.6183313E+110.6183313E+11• AFI( LISBON, SAOPAULO) AFI( LISBON, SAOPAULO) 1.000000 1.000000 0.0000000E+000.0000000E+00• AFI( LISBON, BUONESAIRES) AFI( LISBON, BUONESAIRES) 0.0000000E+00 0.0000000E+00 0.5203010E+110.5203010E+11• AFI( MADRID, SANTIAGO) AFI( MADRID, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.6102913E+110.6102913E+11• AFI( MADRID, SAOPAULO) AFI( MADRID, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.4945099E+110.4945099E+11• AFI( MADRID, BUONESAIRES) AFI( MADRID, BUONESAIRES) 0.0000000E+00 0.0000000E+00 0.5538335E+110.5538335E+11• AFI( PARIS, SANTIAGO) AFI( PARIS, SANTIAGO) 0.0000000E+00 0.0000000E+00 0.6709839E+110.6709839E+11• AFI( PARIS, SAOPAULO) AFI( PARIS, SAOPAULO) 0.0000000E+00 0.0000000E+00 0.5427308E+110.5427308E+11• AFI( PARIS, BUONESAIRES) AFI( PARIS, BUONESAIRES) 0.0000000E+00 0.0000000E+00 0.5958185E+110.5958185E+11

Lingo Çözümü:Lingo Çözümü:

• Row Slack or Surplus Dual PriceRow Slack or Surplus Dual Price• 1 0.4630561E+11 -1.0000001 0.4630561E+11 -1.000000• 2 0.0000000E+00 0.0000000E+002 0.0000000E+00 0.0000000E+00• 3 0.0000000E+00 1.0000003 0.0000000E+00 1.000000• 4 0.0000000E+00 0.0000000E+004 0.0000000E+00 0.0000000E+00• 5 0.0000000E+00 0.0000000E+005 0.0000000E+00 0.0000000E+00• 6 0.0000000E+00 0.0000000E+006 0.0000000E+00 0.0000000E+00• 7 0.0000000E+00 0.0000000E+007 0.0000000E+00 0.0000000E+00• 8 0.0000000E+00 0.0000000E+008 0.0000000E+00 0.0000000E+00• 9 0.0000000E+00 0.0000000E+009 0.0000000E+00 0.0000000E+00• 10 0.0000000E+00 0.0000000E+0010 0.0000000E+00 0.0000000E+00• 11 0.0000000E+00 0.0000000E+0011 0.0000000E+00 0.0000000E+00• 12 0.0000000E+00 -0.4630561E+1112 0.0000000E+00 -0.4630561E+11

TEŞEKKÜRLER :))TEŞEKKÜRLER :))